CHAPTER 8Irrational (Radical) Expressions

PROBLEM 1 Add

4 78428

4 78428

74

72

44 4916

4 272

72747272

PROBLEM 2 Subtract

105 464

105 464 55 232

5 22 5

1

10

2

22

5 2555 2222

10 22

PROBLEM 3 Multiply

3 800090

109

103 102

20106020103

33 10008

3 800090

PROBLEM 4 Divide

3

3

2

168

3

3

2

1683

33

2

828

3

33

2

828

1

88 3

3 88 28 16

PROBLEM 5 Write the general equation

y varies inversely with the cube of x

3x

ky

y varies inversely with the cube of x

PROBLEM 6 Write the particular equation

y varies directly with the ninth root of x;

X = 512, y =20

y varies directly with the ninth root of x;

X = 512, y =209 xky 9 51220 k

k220 10k910 xy

PROBLEM 7 Solve the word problem

If the weight of a box of tissue varies directly

with its volume, and a box of 100 cubicinches weighs 8 ounces, what is the volume

of a box that weighs 24 ounces?

If the weight of a box of tissue varies directly

with its volume, and a box of 100 cubicinches weighs 8 ounces, what is the volume

of a box that weighs 24 ounces?kVw 1008 k

k100

8xy

100

8

x100

824 x300

PROBLEM 8 Solve the word problem, again

Bob's dentist determined the number of cavities developed in his patient's mouth each year is inversely proportional to the total number of minutes spent brushing

during each session.  If Bob developed four cavities during the year he spent only 30

seconds brushing his teeth each time, how many annual cavities will Bob develop if he increases his brushing time to two minutes

per session?

Bob's dentist determined the number of cavities developed in his patient's mouth each year is inversely proportional to the total number of minutes spent brushing during each session.  If Bob developed four cavities during the year he spent only 30 seconds brushing his teeth each time, how many annual cavities will Bob develop if he increases his brushing time to two minutes per session?

m

kC

5.4

k k2

minutes ;2

mm

C2

2C 1C